The Bassone Boat Company manufactures the Water Wiz bass fishing boat. The company purchases the engines it installs in its boats from the Mar-gine Company that specializes in marine engines. Bassone has the following production scheduling for April, May, June, and July:
Month Production
April .........60
May ..........85
June ........100
July .........120
Mar-gine usually manufactures and ships engines to Bassone during the month the engines are due. However, from April through July Mar-gine has a large order with another boat customer and it can only manufacture 40 engines in April, 60 in May, 90 in June, and 50 in July. Margine has several alternative ways to meet Bassone’s production schedule. It can produce up to 30 engines in January, February, and March and carry them in inventory at a cost of $50 per engine per month until it ships them to Bassone. For example, Mar-gine could build an engine in January and ship it to Bassone in April incurring $150 in inventory charges. Mar-gine can also manufacture up to 20 engines in the month they are due on an overtime basis with an additional cost of $400 per engine.
Mar-gine wants to determine the least costly production schedule that will meet Bassone’s schedule.
a. Formulate and solve a linear programming model for this problem.
b. If Mar-gine is able to increase its production capacity in January, February, and March from 30 to 40 engines, what would be the effect on the optimal solution?